Ed Miliband is to say: 'What we saw in Falkirk is the death throes of the old politics. It is a symbol of what is wrong with politics.' Photograph: Stefan Rousseau/PA

Ed Miliband will set out potentially the biggest changes to the Labour-union relationship since the party's formation in 1900 when he proposes on Tuesday that non-party members should be able to vote in party elections, and that its three million union political levy payers can only be involved in the party if they choose to.

Responding to allegations of voting abuse in Falkirk by the party's largest union affiliate, Unite, the Labour leader will say that his reforms, due to be outlined in a speech, mean turning the party's back on unpopular "machine politics".

But the proposals to recast the union link put Miliband's leadership on the line and may be criticised as a diversion of Labour's energies less than two years ahead of a general election.

Miliband will argue the proposals are not designed to break the link with the unions, but instead reinvigorate politics. He will say: "What we saw in Falkirk is the death throes of the old politics. It is a symbol of what is wrong with politics. That was a politics closed, a politics of the machine, a politics hated and rightly so."

Unite's general secretary, Len McCluskey, writing in the Guardian, defends his union's actions, albeit in more emollient language than before. "If Ed Miliband wants to find ways to get more individual trade unionists active in the party, exercising their own judgment on policy and people, I would join with him.

"Done right, this could be a 21st-century way of ensuring working-class influence in the party, just as traditional affiliation has been hitherto," McCluskey says.

The Labour leader's plans also have the longer term potential to reinvigorate cross-party talks on the funding of political parties.

Labour had been opposed to giving trade unionists who pay the political levy the right to choose whether to opt in before some of their dues were used to fund the party.

Miliband is preparing to insist that "Labour wants a closer relationship with millions of working people affiliated to the party through the trade union link".

But he is expected to add they "should no longer be automatically affiliated to the party, but choose as individuals whether they wish to do so".

He will continue: "Trade unions should have political funds for all kinds of campaigns and activities as they choose. But I do not want any individual to be paying money to the Labour Party in affiliation fees unless they have deliberately chosen to do so. I believe we need people to be able to make a more active individual choice on whether they affiliate to the Labour party".

In his second major reform he will propose US-style primaries for parliamentary and mayoral posts in which registered supporters, as well as full party members, are able to vote.

An individual will be able to register for free, or at a minimal sum, deploying a model used by the French Socialist party successfully during its presidential campaigns.

Miliband says that for the case of the London mayoral election in 2016, Labour will choose its candidate through a primary, where voters will either be party members or register as supporters "up to the day of the ballot".

He says he will examine how the same idea can be used "where a sitting MP is retiring and where there are not sufficient members of the local party to make this a properly representative selection process".

Party officials said the proposal to switch to a system of union political levy payers opting into affiliation of the party may see Labour take a financial hit. Most union day to day funding of Labour comes through bulk affiliation of its levy payers, a payment that also gives unions votes at party conference.